分数阶微分谱及其重叠峰信号的定性与定量分析理论

With the deepening of the study in the fields of natural medicine, food, environmental and biological sciences, etc., analysis of complex samples and unknown samples is becoming a trend. Generally, signals obtained from the complex samples or unknown samples are overlapped peak-signals. So, it is a key for qualitative and quantitative analysis of object components to separate it's independent peaks from the overlapped peaks and extract their parameters. This study is very important for qualitative and quantitative analysis of complex samples and unknown samples. In previous study, we found that differential transformation of a signal can enhance the difference of the overlapped peak-signal and can be used for qualitative and quantitative analysis of overlapped peak-signals. In this study, we will frame fractional order derivative spectroscopy and use it to separate the overlapped peak-signals, as a result, a simple and efficient method for qualitative and quantitative analysis of overlapped peak-signals will be proposed. Specific studies include: (1) Filtering method will be explored to preserve signal characteristics (peak position, peak heigh and peak width). (2) In order to obtain fractional derivative spectroscopy of a signal, we are going to design a fractional order differentiator with noise immunity. (3) Qualitative analysis will be explored for overlapped peak-signals. (4) Based on changes of the maxima and zero-crossing values at different order, we will establish a parameter estimation model for each independent peak, as a result, a new theoretical basis will be provided for separation or analysis of complex and unknown smaples by exploring method for quantitative analysis of overlapped peak-signals.

随着天然药物、食品、环境和生物等领域研究的不断深入，需要分析的对象呈现复杂性和未知性，在响应信号上通常表现为一组重叠峰信号。从重叠谱峰信号中分离出独立的子峰信号并提取其特征参数是实现物质组分定性定量分析的关键，对于实现复杂未知样品的定性与定量分析具有重要意义。在前期研究中，我们发现信号的分数阶微分能够不同程度地凸显信号的变化，利用这些变化可实现重叠峰信号的定性与定量分析。在此基础上，本项目创建分数阶微分谱方法，探索重叠峰信号的定性与定量分析理论，得到一种简单、高效的重叠峰信号处理方法，具体内容包括：（1）探索适合信号特征的滤波器方法，保持峰位置、峰高和峰宽不变；（2）设计分数阶微分滤波器，获取信号的分数阶微分谱；（3）研究重叠峰信号的定性分析方法；（4）根据分数阶微分谱的变化规律，建立特征参数估计模型，探索重叠峰信号的定量分析理论，为解决复杂未知样品的分离与分析提供新的理论依据。

随着天然药物、食品、环境和生物等领域研究的不断深入，需要分析的对象呈现复杂性和未知性，在响应信号上通常表现为一组重叠峰信号。从重叠谱峰信号中分离出独立的子峰信号并提取其特征参数是实现物质组分定性定量分析的关键，对于实现复杂未知样品的定性与定量分析具有重要意义。..为了实现重叠峰信号的定性、定量分析，本项目开展了四个方面的工作：（1）探索保峰平滑方法；（2）设计具有噪声免疫力的分数阶微分滤波器，获取信号的分数阶微分谱；（3）谱峰增强与检测的定性分析方法研究；（4）谱峰定量分析的参数提取方法研究。取得了如下成果：（1）为了保护峰位置在信号平滑中不被改变，通过设计扩散函数来控制扩散过程，给出了一种适合重叠峰信号的保峰平滑算法；（2）借助分数阶微分，通过改进常规扩散方程，提出了时间分数阶扩散滤波方法，因为分数阶微分的非局部性，使得时间分数阶扩散滤波比常规扩散滤波具有更好的效果；（3）为了克服噪声对分数阶微分的影响，利用卷积的性质结合高斯函数，设计出了具有噪声免疫力的分数阶微分器，该微分器可直接获取噪声信号的分数阶微分谱；（4）利用正交小波对信号进行分解，通过构造正交小波的分数阶微分运算矩阵，给出了一种基于运算矩阵的分数阶微分实现方法；（5）为了更好地分辨出信号峰，通常需要对信号进行增强处理，然而，噪声会严重影响分辨效果，为此，提出了一种具有噪声免疫力的重叠峰信号增强方法，用以改善重叠峰信号的分辨；（6）以锐化后的峰顶为中心，选取部分 点，并根据事先确定的峰型函数，通过线性拟合得到各个子峰的初始峰形参数，然后根据检测到的峰数目和各个峰的初始参数，在给定模型下，利用最优化方法获取重叠峰信号的真实参数，从而给出了一种重叠峰信号的定量分析方法。